Water Level and Exponential Functions

The video tutorial explains the decline in Lake Yoda's water level since 2002, starting at a record high of 450 feet and decreasing by 3.3% annually. It demonstrates how to model this change using an exponential function and solve for the year when the water level will reach 225 feet. The process involves setting up an equation, converting it to logarithmic form, and calculating the year using the change of base formula. The result shows that the water level will reach 225 feet around the year 2023.

What was the record high water level of Lake Yoda in 2002?

• 225 feet

• 300 feet

• 450 feet

• 500 feet

What is the initial value 'a' in the exponential function for Lake Yoda's water level?

• 3.3

• 0.967

• 450

• 225

What is the decay factor 'b' in the exponential function for Lake Yoda's water level?

• 1.033

• 1.967

• 0.033

• 0.967

What equation is used to determine when the water level will reach 225 feet?

• 225 = 450 * 0.967^t

• 450 = 225 * 0.967^t

• 225 = 450 * 1.033^t

• 450 = 225 * 1.033^t

How do you express the exponential equation as a logarithmic equation?

• log base 0.967 of 1.5 = t

• log base 0.5 of 0.967 = t

• log base 0.967 of 0.5 = t

• log base 1.033 of 0.5 = t

What is the change of base formula used to solve the logarithmic equation?

• log(0.967) / log(0.5)

• log(1.033) / log(0.5)

• log(0.5) / log(1.033)

• log(0.5) / log(0.967)

Approximately how many years will it take for the water level to reach 225 feet?

• 25 years

• 23 years

• 21 years

• 19 years

What is the base year used to calculate the exact year when the water level will reach 225 feet?

• 2000

• 2002

• 2001

• 2003

In what year is the water level expected to reach 225 feet?

• 2023

• 2024

• 2022

• 2021

If the water level continues to drop at 3.3% per year, what will be the approximate water level in 2023?

• 225 feet

• 300 feet

• 350 feet

• 400 feet